Modelling of transverse vibration of beam of linearly variable depth with edge crack

In this paper modelling of transverse vibration of a beam of linearly varia ble depth and constant thickness in the presence of an 'open' edge crack no rmal to its axis has been proposed using the concept of a rotational spring to represent the crack section and the Frobenius method to enable possible detection of location of the crack based on the measurement of natural fre quencies. The method can also be used to solve the forward problem. A numbe r of numerical examples are presented involving cantilever beams to show th e effectiveness of the method for the inverse problem. The error in the pre diction of crack location is less than 2% and size is around 10% for all lo cations except at the fixed end. Crack sizes 10-50% of section depth have b een examined. (C) 1999 Elsevier Science Ltd. All rights reserved.